EE1427 Engineering Science – Dr. Daniel Nankoo
Tutorial 8
8. Temperature and Heat – Tutorial 8
8.1
The SR-71 Blackbird, which is 107 feet 5 inches long, is the world’s fastest airplane. It can fly
at three times the speed of sound (Mach 3) at altitudes of 80,000 ft. When it lands after a long flight, it
is too hot to be touched for about 30 minutes, and is 6.0 inches longer than at takeoff. How hot is the
Blackbird when it lands, assuming its coefficient of linear expansion is 24 × 10 −6 K −1 and its
temperature at takeoff is 23 °C? (220°C)
8.2
The world’s longest suspension bridge is the Akashi Kaikyo Bridge in Japan. The bridge is
3910 m long and is constructed of steel. How much longer is the bridge on a warm summer day (30.0
°C) than on a cold winter day ( −5.00 º C)? (1.6m)
8.3
A hole in an aluminium plate has a diameter of 1.178cm at 23.00 °C. (a) What is the diameter
of the hole at 199.0 °C? (b) At what temperature is the diameter of the hole equal to 1.176cm?
(1.183cm, -48°C)
It is desired to slip an aluminium ring over a steel bar (Figure 8.4). At 10.00 °C the inside
8.4
diameter of the ring is 4.000 cm and the diameter of the rod is 4.040 cm. (a) In order for the ring to slip
over the bar, should the ring be heated or cooled? Explain. (b) Find the temperature of the ring at which
it fits over the bar. The bar remains at 10.0 °C. (430°C)
Figure 8.4
8.5
At 12.25 °C a brass sleeve has an inside diameter of 2.19625cm and a steel shaft has a
diameter of 2.19893cm. It is desired to shrink-fit the sleeve over the steel shaft. (a) To what
temperature must the sleeve be heated in order for it to slip over the shaft? (b) Alternatively, to what
temperature must the shaft be cooled before it is able to slip through the sleeve? (76°C, -89°C)
8.6
Early in the morning, when the temperature is 5.0 °C, petrol is pumped into a car’s 51-L steel
petrol tank until it is filled to the top. Later in the day the temperature rises to 25 °C. Since the volume
of petrol increases more for a given temperature increase than the volume of the steel tank, petrol will
spill out of the tank. How much petrol spills out in this case? (0.93L)
8.7
Some cookware has a stainless steel interior (α = 17.3 × 10 −6 K −1 ) and a copper bottom
(α = 17.0 × 10 −6 K −1 ) for better heat distribution. Suppose an 8inch pot of this construction is heated to
610 °C on the stove. If the initial temperature of the pot is 22 °C, what is the difference in diameter
change for the copper and the steel? (0.0014in)
8.8
You construct two wire-frame cubes, one using copper wire, the other using aluminium wire.
At 21 °C the cubes enclose equal volumes of 0.016 m 3 . (a) If the temperature of the cubes is increased,
which cube encloses the greater volume? (b) Find the difference in volume between the cubes when
their temperature is 97 °C. (2.6×10-5m3)
8.9
A copper ball with a radius of 1.6 cm is heated until its diameter has increased by 0.18 mm.
Assuming an initial temperature of 22 °C, find the final temperature of the ball. (680°C)
8. Temperature and Heat
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EE1427 Engineering Science – Dr. Daniel Nankoo
Tutorial 8
8.10
An aluminium saucepan with a diameter of 23 cm and a height of 6.0 cm is filled to the brim
with water. The initial temperature of the pan and water is 19 °C. The pan is now placed on a stove
burner and heated to 88 °C. (a) Will water overflow from the pan, or will the water level in the pan
decrease? Explain. (b) Calculate the volume of water that overflows or the drop in water level in the
pan, whichever is appropriate. (24cm3)
8.11
How much heat is required to raise the temperature of a 55-g glass ball by 15 C°? (0.69kJ)
8.12
A 5.0-g lead bullet is fired into a fence post. The initial speed of the bullet is 250 m/s, and
when it comes to rest, half its kinetic energy goes into heating the bullet. How much does the bullet’s
temperature increase? (120K)
8.13
Silver pellets with a mass of 1.0 g and a temperature of 85 °C are added to 220 g of water at
14 °C. (a) How many pellets must be added to increase the equilibrium temperature of the system to 25
°C? Assume no heat is exchanged with the surroundings. (b) If copper pellets are used instead, does the
required number of pellets increase, decrease, or stay the same? Explain. (c) Find the number of copper
pellets that are required. (722, 436)
8.14 A 235-g lead ball at a temperature of 84.2 °C is placed in a light calorimeter containing 177 g
of water at 21.5 °C. Find the equilibrium temperature of the system. (23.9°C)
8.15 If 2200 J of heat is added to a 190-g object, its temperature increases by 12 C°. (a) What is the
heat capacity of this object? (b) What is the object’s specific heat? (0.18kJ/°C, 0.96kJ/kg.K)
8.16
An 87.6-g lead ball is dropped from rest from a height of 5.43 m. The collision between the
ball and the ground is totally inelastic. Assuming all the ball’s kinetic energy goes into heating the ball,
find its change in temperature. (0.416°C)
8.17
To determine the specific heat of an object, a student heats it to 100 °C in boiling water. She
then places the 38.0-g object in a 155-g aluminium calorimeter containing 103 g of water. The
aluminium and water are initially at a temperature of 20.0 °C, and are thermally insulated from their
surroundings. If the final temperature is 22.0 °C, what is the specific heat of the object? Identify the
material in the object. (385J/kg.K)
8.18
At the local county fair, you watch as a blacksmith drops a 0.50-kg iron horseshoe into a
bucket containing 25 kg of water. (a) If the initial temperature of the horseshoe is 450 °C, and the
initial temperature of the water is 23 °C, what is the equilibrium temperature of the system? Assume no
heat is exchanged with the surroundings. (b) Suppose the 0.50-kg iron horseshoe had been a 1.0-kg
lead horseshoe instead. Would the equilibrium temperature in this case be greater than, less than, or the
same as in part (a)? Explain. (24°C)
8.19
The ceramic coffee cup in Figure 8.19, with m = 116 g and c = 1090 J (kg ⋅ K), is initially at
room temperature (24.0 °C). If 225 g of 80.3 °C coffee and 12.2 g of 5.00 °C cream are added to the
cup, what is the equilibrium temperature of the system? Assume that no heat is exchanged with the
surroundings, and that the specific heat of coffee and cream are the same as the specific heat of water.
(70.5°C)
Figure 8.19
8. Temperature and Heat
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EE1427 Engineering Science – Dr. Daniel Nankoo
Tutorial 8
8.20
Find the heat that flows in 1.0 s through a lead brick 15 cm long if the temperature difference
between the ends of the brick is 8.5 C°. The cross-sectional area of the brick is 12 cm 2 . (2.3J)
8.21
Two metal rods of equal length—one aluminium, the other stainless steel—are connected in
parallel with a temperature of 20.0 °C at one end and 118 °C at the other end. Both rods have a circular
cross section with a diameter of 3.50 cm. (a) Determine the length the rods must have if the combined
rate of heat flow through them is to be 27.5 J per second. (b) If the length of the rods is doubled, by
what factor does the rate of heat flow change? (0.80m)
8.22
Two cylindrical metal rods—one copper, the other lead—are connected in parallel with a
temperature of 21.0 °C at one end and 112 °C at the other end. Both rods are 0.650 m in length, and the
lead rod is 2.76 cm in diameter. If the combined rate of heat flow through the two rods is 33.2 J/s, what
is the diameter of the copper rod? (2.64cm)
8.23 Two metal rods—one lead, the other copper—are connected in series, as shown in Figure
8.23. Each rod is 0.525 m in length and has a square cross section 1.50 cm on a side. The temperature
at the lead end of the rods is 2.00 °C; the temperature at the copper end is 106 °C. (a) The average
temperature of the two ends is 54.0 °C. Is the temperature in the middle, at the lead-copper interface,
greater than, less than, or equal to 54.0 °C? Explain. (b) Given that the heat flow through each of these
rods in 1.00 s is 1.41 J, find the temperature at the lead-copper interface. (98°C)
Figure 8.23
8.24
Consider two cylindrical metal rods with equal cross section—one lead, the other
aluminium—connected in series. The temperature at the lead end of the rods is 20.0 °C; the
temperature at the aluminium end is 80.0 °C. (a) Given that the temperature at the lead-aluminium
interface is 50.0 °C, and that the lead rod is 14 cm long, what condition can you use to find the length
of the aluminium rod? (b) Find the length of the aluminium rod. (89cm)
8.25 A copper rod 85 cm long is used to poke a fire. The hot end of the rod is maintained at 105 °C
and the cool end has a constant temperature of 21 °C. What is the temperature of the rod 23 cm from
the cool end? (44°C)
8.26 Two identical objects are placed in a room at 21 °C. Object 1 has a temperature of 95 °C and
object 2 has a temperature of 25 °C. What is the ratio of the net power emitted by object 1 to that
radiated by object 2? (26)
8.27
A block has the dimensions L, 2L, and 3L. When one of the L × 2 L faces is maintained at the
temperature T1 and the other L × 2 L face is held at the temperature T2 , the rate of heat conduction
through the block is P. Answer the following questions in terms of P. (a) What is the rate of heat
conduction in this block if one of the L × 3 L faces is held at the temperature T1 and the other L × 3 L
face is held at the temperature T2 ? (b) What is the rate of heat conduction in this block if one of the
2 L × 3 L faces is held at the temperature T1 and the other 2 L × 3 L face is held at the temperature T2 ?
(9/4 P, 9P)
8. Temperature and Heat
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